I've been trying to work some CFA-s for various first order latent constructs with AMOS, on a relatively large sample of N=1500 (approximatively) and, following the recommendations from Byrne (2001) Structural equation modelling with AMOS, I have first covariated error terms that had very high MI, and then; looked for items that had very high covariances in the standardized covariance matrix (>2.58) and eliminated them (at which point, my CFA, according to Byrne, turned into an exploratory factor analysis), yet, despite all these constraints, I have never reached a large "majority" of good fit indices - I used CMIN/df; RMSEA; PCLOSE; CFI; GFI, AGFI while being in danger of thinning my scales down to two items each.
All my initial .sav files were cleaned of all missing values.
My questions would then be : When does one stop trying to optimize model fit by adding constraints to the model? Are there other types of constraints that one might add?
I'll just add that I did not compare my model (which contains, for one of the constructs - motivation for instance, measured with a scale derrived from Self-determination theory - 4 factors) with one with three or two factors. I only took the default references given by AMOS: the saturated and the independent models.
Thank you kindly for your suggestions!
Since my initial EFA-s for most of these models worked just fine